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Please see Chapter 10 of Valuing Fixed Income Investments & Derivative Securities by Steven L Allen & Arnold D Kleinstein, New York Institute of Finance ISBN 0-13-931775-9 (ed 1991).

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Q: How can you value a bond having long and short coupon at the beginning and at the end respectively?
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What is the size of the short coupon bond?

A short coupon bond is 8.5 x 11.


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Zero Coupon Bonds?

When you buy a standard bond you invest in an instrument that pays interest. The rate of interest paid is also known as the coupon rate, or just coupon for short. If you invest $10,000 in bonds priced at par, or 100, with a coupon of 3%, you know you'll receive 3% annually and get your principal back at par upon maturity. So if you are an astute reader and you noticed the title of this post you know it has something to do with zero coupon bonds. According to what we know about how bonds work why would anybody put their money into a bond that doesn't' pay interest? It's true that zeroes don't pay out in regular interest payments like bonds that pay a coupon. But that doesn't mean you don't get compensated for your investment. The way a zero coupon bond works is that you buy it at an initial discount to par and upon maturity you receive par. As an example, let's assume you wanted to buy $10,000 worth of zero coupon bonds. Instead of receiving a price of par, or 100, you're given a discounted price of, say, 85. This means that if you invest $8,500 now, upon maturity you'll receive the full $10,000. The difference between what you paid and the maturity amount becomes your interest income. The bonds are assumed they are earning interest each year even though they don't pay you any actual money. In bondspeak this is referred to as the bond's accretion. One catch here is that the IRS still charges you income tax on that theoretical income. It calls it imputed income. One way to legally sidestep having to pay income tax on accreted income is to invest in zeroes within your IRA, 401(k), or other tax sheltered investment account. One of the benefits (or drawbacks) to zero coupon bonds is that you don't have actual money coming to you that you must reinvest at current rates. This can work to your advantage if you bought your zero before rates fell because instead of having to reinvest your income at new lower rates you're locked in. However, the opposite is true if rates rise and that can be a major drawback to zeroes. Since they return absolutely nothing to you until maturity they are much more sensitive to interest rate fluctuations than standard bonds. The longer maturity on the zero the greater this amplified effect can be. On a long maturity zero coupon bond you are locking in a rate of interest not only for your principal but also on the imputed income for a long period of time. You don't have the option to invest the income spun off the bond at different rates so you are much more affected by interest rate changes than an investor in regular bonds for the total length of time to maturity.

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